Conventionally, the nearest neighbor method and bilinear interpolation have been used widely as interpolation methods to obtain a match between a high definition liquid crystal display (LCD) and a lower resolution personal computer (PC) screen. These interpolation methods are popular because only a small number of calculations is required for the real time processing of a high resolution image. However, it is known that the nearest neighbor method contributes to an increase in distortion in an expanded image, and therefore, the bilinear interpolation method, whereby the rough shape of an original image can be expanded, is often employed. But it is also true that bilinear interpolation tends to blur resultant images, an effect that is especially remarkable when bilinear interpolation is employed for images displayed on an image display device, such as an LCD, that does not have the low-pass characteristics.
The bilinear interpolation method is an example of the multirate processing theory called linear interpolation. And because of this, interpolation methods based on the general multirate processing theory have been proposed that use more pixels than the number employed for bilinear interpolation. For example, a multirate interpolation method using a table search method for a linear filter is disclosed in U.S. Pat. No. 5,410,616. Further, in U.S. Pat. No. 5,594,676, linear filters having different orders are prepared, and are changed in accordance with the characteristics exhibited by peripheral pixels. In addition, according to reference document 1 (IEEE Signal Processing Magazine, Vol. 16, No. 6, pp. 22-38, November 1999), pertaining to the generalization of the interpolation method, except for a point for obtaining an efficient number of calculations, a linear interpolation method whereby information loss can theoretically be minimized can be substantially provided as an interpolation method that uses a third-order B-spline. Thus, it becomes apparent that image processing using the linear interpolation method is approaching the limit of its effectiveness.
When the above method is employed for image interpolation, vertical calculations and horizontal calculations are sequentially performed, and one pixel in a low-resolution image is transformed into a set of rectangular pixel regions, so that the appearance of step-shapes or chain-shapes of oblique lines can not be prevented. In order to prevent the appearance of such shapes, it is considered effective to perform interpolation by employing a directional filter that uses peripheral pixels aligned in the direction in which an oblique line is extended. For example, in reference document 2 (IEEE Proceedings of the 1995 International Conference on Acoustics, Speech, and Signal Processing, Vol. 4, pp. 2383-2386, May 1995), and in U.S. Pat. No. 5,991,463, the use of the directional, linear interpolation methods are proposed.
These image expansion methods are required for a computer monitor and a projector in order to provide a match between a flat panel display, such as an LCD, which has a fixed pixel resolution, and an image produced by the graphics card of a PC. However, when an expansion process for an original image is performed vertically and horizontally, or in the opposite order, as with the conventional bilinear interpolation method, correlation is increased vertically and horizontally for the pixels that have been interpolated. As a result, when an oblique line is expanded, a pixel displayed on a low-resolution screen is transformed into a group of rectangular pixel regions, and a step-shape or chain-shape of oblique line appears. And even when a high accurate linear interpolation is performed using a third order B-spline, the above phenomenon becomes ever more remarkable as the expansion ratio is increased. When this phenomenon appears on the display of a high definition LCD, it seems to the user that the physical definition of the output screen differs from the actual definition.
In reference document 2, the differences in pixels are calculated for predetermined directions, and the reciprocals of values obtained for all the directions are added together to acquire the normalized weight coefficient. Linear interpolation is performed for pixels dispersed in each direction corresponding to each weight coefficient, and to provide an expanded image, the summation of the results is calculated based on the weight coefficients. In this method, linear interpolation is performed by regarding, as the dominant direction, the one in which the pixel difference is small, and this method can be considered as a method for preventing the step-shapes or chain-shapes of oblique lines. However, using this method, since in order to prevent an erroneous determination the summation is calculated by also using the interpolation results obtained for the non-dominant direction, blurring of an output image can not be avoided.
In U.S. Pat. No. 5,991,463, a bilinear interpolation technique using four adjacent pixels arranged in a specific direction is proposed as a directional interpolation method. Specifically, according to this method, first, a difference among four peripheral pixels is obtained for the determination of three directions, i.e., the right oblique, the left oblique and the vertical directions. The differences are compared with each other, and the direction having the smallest pixel difference is determined to be an interpolation direction. In addition, an additional search is performed, as needed. When the pixel differences for the three directions are substantially the same, the vertical direction is determined. When the pixel difference for the vertical direction is small and the difference for one of the oblique directions is obviously small, the pertinent oblique direction is determined. When the pixel differences for the two oblique directions are small, the same direction determination is performed for a pixel that forms an oblique line parallel to the pixels whose difference was calculated. And when the differences for the two oblique directions are small for the additional pixel, the vertical direction is determined. In this manner, as is disclosed in this publication, when interpolation is performed for one specific direction, excessive image blurring can be avoided.
However, according to the above method, an erroneous determination may be made if in an observation pixel mask used for direction determination foreground and background can not be identified, such as when white and black pixels intersect to form an X shape. When the direction can not be correctly determined, an interpolation value is obtained that is far different from the correct value, and there is a defect in the interpolation results. In addition, generally, according to the expansion method for which only oblique interpolation is performed, correlation in the vertical and horizontal directions is reduced. That is, since at the point where vertical and horizontal linear lines intersect, an image is expanded as if it is assumed as a diamond shape, instead of expanding in the original vertical and horizontal directions, the obtained image is distorted. Further, since the isolated point of the original image is determined to be the point whereat the oblique lines cross, and the image is to be expanded in the oblique directions, the isolated point is faded out, or the expansion of the image is less than it is supposed to be.
To resolve the above shortcomings, it is one object of the present invention to provide an image transform method whereby the step-shapes or chain-shapes of oblique lines are not remarkable, even when an image has been expanded by two or more times of its original size.
It is another object of the present invention to output a clear, expanded image wherein distortion is eliminated and no constituent lines of fonts and graphics are missing. It is an additional object of the present invention to perform fast image transform processing.